Economic Environment, The Bankruptcy Of Several Types Of Discrete Risk Model Distribution

The classical risk model has been studied more than one hundred years. At present it is nearly perfect and the exact calculated results for all the atuarial diagnostics are derived in closed form. With the development of risk model, economic environment has far greater influence on bankruptcy theory than it used to, which can not be neglected. The economic factors such as investment income and interest rate play an important role in the financial stability of insurance companies. In addition, the scale of the business expands incessantly and the types of insurance increase.This thesis mainly deals with classical risk model which is affected by three facors.In chapter 1, we briefly review the risk theory and its development.In chapter 2, a discrete risk model with return on investments is proposed by putting a random return on investment in the compound binomial model. The integral equation of its ruin probability is derived. Recursive formulas are provided for the the joint distribution of the surplus immediately before ruin and the deficit at ruin. The common formula of its ultimate ruin probability and Lundberg'sinequality are obtained.In chapter 3, a discrete double-type risk model is built up and discussed. One counting process of claim is compound poisson process, the other is compound binomial process. At the same time the counting process of premium is poisson process, while the rate of premium income is regarded as a random variable not a constant. The properties of surplus process are discussed, ajustment coefficient equation and the upper bound of probability is obtained.In chapter 4, discrete risk model under the effect of stochastic interest rates is mainly studied. Firstly, ruin distribution is discussed in one-type insurance model which is generalized to a correlated claims risk model. Secondly, a integral equation for the ultimate ruin probability is obtained in the risk model. Then, the formulas of ultimate ruin probability and Lundberg inequality for this model are given by means of martingle theory. Finally, an integral equation of the ruin probability and some ralated formulas are got under given that interest rates are zero.